Two‐scale topology optimization for composite plates with in‐plane periodicity

Summary This study proposes a two‐scale topology optimization method for a microstructure (an in‐plane unit cell) that maximizes the macroscopic mechanical performance of composite plates. The proposed method is based on the in‐plane homogenization method for a composite plate model in which the macrostructure is modeled using thick plate theory and the microstructures are three‐dimensional solids. Macroscopic plate characteristics such as homogenized plate stiffnesses and generalized thermal strains are evaluated through the application of numerical plate tests applied to an in‐plane unit cell. To handle large rotations of the composite plates, we employ a co‐rotational formulation that facilitates working with the two‐scale plate model formulated within a small strain framework. Two types of objective functions are tested in the presented optimization problems: one minimizes the macroscopic end compliance to maximize the macroscopic plate stiffness, whereas the other maximizes components of a macroscopic nodal displacement vector. Analytical sensitivities are derived based on in‐plane homogenization formulae so that a gradient‐based method can be employed to update the topology of in‐plane unit cells. Several numerical examples are presented to demonstrate the proposed method's capability related to the design of optimal in‐plane unit cells of composite plates. Copyright © 2017 John Wiley & Sons, Ltd.